"if you think childlike, you'll stay young. If you keep your energy going, and do everything with a little flair, you're gunna stay young. But most people do things without energy, and they atrophy their mind as well as their body. you have to think young, you have to laugh a lot, and you have to have good feelings for everyone in the world, because if you don't, it's going to come inside, your own poison, and it's over" Jerry Lewis
"I don’t believe
in the irreversibility of situations" Deleuze

Note on Citations

The numerical citations refer to page number. The source's text-space (including footnote region) is divided into four equal portions, a, b, c, d. If the citation is found in one such section, then for example it would be cited p.15c. If the cited text lies at a boundary, then it would be for example p.16cd. If it spans from one section to another, it is rendered either for example p.15a.d or p.15a-d. If it goes from a 'd' section and/or arrives at an 'a' section, the letters are omitted: p.15-16.

[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

Henry Somers-Hall

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

Part 3: Beyond Representation

Chapter 6: Hegel and Deleuze on Ontology and the Calculus

Subdivision 1: Introduction

Brief Summary:

Deleuze’s and Hegel’s anti-representationalist philosophies can be compared on the basis of their different interpretations of differential calculus and Kant’s antinomies.

Summary

In the previous section, we examined Deleuze’s and Hegel’s responses to the problems in Aristotle’s and Kant’s representational systems. Both Deleuze and Hegel make use of a concept of unifying difference. Deleuze’s is based on Bergson’s duration, a continuously-integrated heterogeneous multiplicity. Hegel’s is based on his dialectics, a process of productive oppositions united through their genetic relations.

Now we look more at the relation between Deleuze and Hegel, in particular, how each one might criticize the other. To do this we need a common basis for the comparison. “The present chapter will relate Hegel and Deleuze mediately through their different interpretations of the calculus and Kant's antinomies.” (161) For Hegel, calculus expresses what he calls the Notion. Calculus was based on infinite numbers until Weierstrass made it possible for calculus to be based on set theory, and this opened a new path for Russell’s philosophy.

for Deleuze as well as Hegel, what is important about the calculus is to be found in the "so-called barbaric or pre-scientific interpretations" (DR, 170). I n fact, for Deleuze, the calculus is even more central to his philosophy, since an interpretation of the calculus that moves away from the set-theoretic, and therefore spatial, understanding of mathematics opens the way for a philosophy of difference that truly understands difference apart from representation. As we shall also see, Hegel and Deleuze's interpretations of the antinomies mirror those of the calculus and show the applications of these principles outside of the mathematical realm. (162)